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On passing thorugh a telescope a flux of...

On passing thorugh a telescope a flux of light increases its intensity `eta = 4.0.10^(4)` times. Find the angular dimension of a distance object if its image formed by that telescope has an angualr dimension `Psi = 2.0^(@)`.

Text Solution

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It is clear from the figure that a parallel beam of light, originally of intensity `I_(0)` has, no emerging from the telescope, an intensity.
`I = I_(0) ((f_(0))/(f_(e)))^(2)`
because it is concentrated over a section whose diameter is `f_(e)//f_(0)` of the diameter of the cross section of the incident beam.

Thus `eta = ((f_(0))/(f_(e)))^(2)`
So `T = (f_(0))/(f_(e)) = sqrt(eta)`
Now `T = (tan Psi')/(tan Psi) = (Psi')/(Psi)`
Hence `Psi = Psi' //sqrt(eta) = 0.6`' on substitution.
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